[HN Gopher] Is Mathematics Invented or Discovered? (2020) [video] ___________________________________________________________________ Is Mathematics Invented or Discovered? (2020) [video] Author : janandonly Score : 17 points Date : 2023-11-14 20:44 UTC (2 days ago) (HTM) web link (www.youtube.com) (TXT) w3m dump (www.youtube.com) | Mimmy wrote: | I went to an in-person Q&A featuring a Fields medalist. The | audience was a collection of undergraduate and high school math | students, with a few professors in attendance. | | One of the young students asked exactly this question to which | everyone in the audience collectively groaned. The Fields | medalist gave a short answer, something along the lines of "I | don't know a single mathematician that thinks it's invented." | | He was being polite, but you could tell he didn't think there was | anything else interesting to say. | pa7x1 wrote: | It's both. The axioms are invented, the corpus of theorems is | discovered. As once the axioms are chosen the provable theorems | are already fixed. | | But the axioms are a choice, and we can pick different ones. | The common choice of axioms is utilitarian, they lead to | interesting math that helps us describe the universe. | random3 wrote: | Are the theories beyond axiom fundamentally different if | axioms are changed, though? And if not, aren't then axioms | merely props or placeholders for invariants? | sweezyjeezy wrote: | I'm not sure I see why the axioms were not also discovered | though? Choice between irreducible assumptions does not seem | to make them any more 'invented'. | Mimmy wrote: | I would agree the axioms are chosen, but what's the | connection between choosing something and inventing it? | | Choosing to study molecular biology doesn't mean cells are a | human invention. | photochemsyn wrote: | Different sets of axioms open the doors to different mathematical | universes? I'm given to understand that's the general concensus | on what Godel's incompleteness theorems mean, practically | speaking. | lupire wrote: | Is a new pharmaceutical invented or discovered? How about a new | iPhone? | | This is linguistics, not science. | svara wrote: | Are space ships in game of life invented or discovered? I've come | to believe that's ultimately exactly the same question. | | We're talking about rich structures that emerge from simple rule | sets. That's really all there is to mathematics. | | We started from structures that provide helpful abstractions for | things in real life, which might lead some to believe that | mathematics points to some hidden reality behind things, but | that's ultimately just spiritual thinking in rational sounding | clothing. | dang wrote: | Url changed from https://abakcus.com/video/roger-penrose-is- | mathematics-inven..., which points to this. | dang wrote: | Discussed at the time: | | _Roger Penrose - Is Mathematics Invented or Discovered? [video]_ | - https://news.ycombinator.com/item?id=22896671 - April 2020 (311 | comments) ___________________________________________________________________ (page generated 2023-11-16 23:00 UTC)